In this paper, we give novel certificates for triangular equivalence and rank profiles. These certificates enable to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible overall overhead. We first provide quadratic time and space non-interactive certificates saving the logarithmic factors of previously known ones. Then we propos...

In this paper, we design a new model of preconditioner for systems of linear equations. The convergence properties of the proposed methods have been analyzed and compared with the classical methods. Numerical experiments of convection-diffusion equations show a good im- provement on the convergence, and show that the convergence rates of proposed methods are superior to the other modified itera...

This article investigates observability/controllability of a networked dynamic system (NDS) in which matrices its subsystems are expressed through linear fractional transformations (LFTs). Some relations have been obtained between this NDS and descriptor systems about their observability/controllability. A necessary sufficient condition is established with the associated depending affinely on s...

The asymptotic convergence of parameterized variants of Newton’s method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to zero as the iteration proceeds. The exact local solutions to the perturbed systems then form a differentiable path leading to a solution of the origin...

Carrier-phase ambiguity resolution is usually based on the assumption that the underlying model of observation equations is of full rank. In this contribution the model of observation equations is assumed to be of less than full rank. The well-known three-step procedure of integer least squares is generalized and it is shown how the solution can be affected by the rank deficiency. Although the ...

In this paper we describe the Garnier systems as isomonodromic deformation equations of a linear system with a simple pole at 0 and a Poincaré rank two singularity at infinity. We discuss the extension of Okamoto’s birational canonical transformations to the Garnier systems in more than one variable and to the Schlesinger systems.

In this paper a new class of simplified low-cost analog artificial neural networks with on chip adaptive learning algorithms are proposed for solving linear systems of algebraic equations in real time. The proposed learning algorithms for linear least squares (LS), total least squares (TLS) and data least squares (DLS) problems can be considered as modifications and extensions of well known alg...